Some properties of cumulative Tsallis entropy

Calì, Camilla; Longobardi, Maria; Ahmadi, Jafar

doi:10.1016/j.physa.2017.05.063

Cited by 40 publications

(30 citation statements)

References 24 publications

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“…is the partition entropy of X evaluated at x. As an extension of cumulative entropy, Ahmadi [5] presented the concept of cumulative Tsallis entropy for random variable X as follows:…”

Section: Partial Tsallis Entropy Of Uncertain Random Variablesmentioning

confidence: 99%

“…Example 2 Let η be a random variable such that η ∼ Exp (5). Also, suppose that τ is an uncertain variable with uncertainty distribution N (2, 3).…”

Section: Monte Carlo Simulation For Partial Tsallis Entropymentioning

confidence: 99%

“…As an extension of Shanon (logarithm) entropy, Tsallis [25] introduced the concept of Tsallis entropy. In order to measure the indeterminacy of random lifetime variables, several authors proposed different types of cumulative and cumulative residual entropy, for instance [5,9,10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tsallis entropy of uncertain random variables and its application

Ahmadzade

Rezaei

et al. 2021

Soft Comput

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Tsallis entropy ia a flexible extension of Shanon (logarithm) entropy. Since, entropy measures indeterminacy of an uncertain random variable, this paper proposes the concept of partial Tsallis entropy for uncertain random variables as a flexible devise in chance theory. An approach for calculating partial Tsallis entropy for uncertain random variables, based on Monte-Carlo simulation, is provided. As an application in finance, partial Tsallis entropy is invoked to optimize portfolio selection of uncertain random returns via crow search algorithm.

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“…is the partition entropy of X evaluated at x. As an extension of cumulative entropy, Ahmadi [5] presented the concept of cumulative Tsallis entropy for random variable X as follows:…”

Section: Partial Tsallis Entropy Of Uncertain Random Variablesmentioning

confidence: 99%

“…Example 2 Let η be a random variable such that η ∼ Exp (5). Also, suppose that τ is an uncertain variable with uncertainty distribution N (2, 3).…”

Section: Monte Carlo Simulation For Partial Tsallis Entropymentioning

confidence: 99%

See 1 more Smart Citation

Tsallis entropy of uncertain random variables and its application

Ahmadzade

Rezaei

et al. 2021

Soft Comput

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“…The entropy has been widely adopted, specifically the classical formulations and their most common generalizations. Moreover, we can mention the Rényi [42], Tsallis [9], residual [14], cumulative [12] and past [36] entropies, as well as extropies [2], and other closely related indices [21,55].…”

Section: Introductionmentioning

confidence: 99%

Entropy analysis of human death uncertainty

Machado

Lopes

2021

Nonlinear Dyn

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Uncertainty about the time of death is part of one’s life, and plays an important role in demographic and actuarial sciences. Entropy is a measure useful for characterizing complex systems. This paper analyses death uncertainty through the concept of entropy. For that purpose, the Shannon and the cumulative residual entropies are adopted. The first may be interpreted as an average information. The second was proposed more recently and is related to reliability measures such as the mean residual lifetime. Data collected from the Human Mortality Database and describing the evolution of 40 countries during several decades are studied using entropy measures. The emerging country and inter-country entropy patterns are used to characterize the dynamics of mortality. The locus of the two entropies gives a deeper insight into the dynamical evolution of the human mortality data series.

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“…Recently, several measures of discrimination and uncertainty have been proposed in the literature (see, for instance, [ 13 , 14 , 15 , 16 , 17 , 18 , 19 ]). In particular, in the context of the Dempster–Shafer evidence theory, there are interesting measures of discrimination, as the Deng entropy; it was this latter concept that has suggested us the introduction of a dual definition.…”

Section: Introductionmentioning

confidence: 99%

A Dual Measure of Uncertainty: The Deng Extropy

Buono

Longobardi

2020

Entropy

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The extropy has recently been introduced as the dual concept of entropy. Moreover, in the context of the Dempster–Shafer evidence theory, Deng studied a new measure of discrimination, named the Deng entropy. In this paper, we define the Deng extropy and study its relation with Deng entropy, and examples are proposed in order to compare them. The behaviour of Deng extropy is studied under changes of focal elements. A characterization result is given for the maximum Deng extropy and, finally, a numerical example in pattern recognition is discussed in order to highlight the relevance of the new measure.

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Some properties of cumulative Tsallis entropy

Cited by 40 publications

References 24 publications

Tsallis entropy of uncertain random variables and its application

Tsallis entropy of uncertain random variables and its application

Entropy analysis of human death uncertainty

A Dual Measure of Uncertainty: The Deng Extropy

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